Rudy found himself pushed down the pecking order at Bayern following the champions' signing of Goretzka, who he will now replace at Schalke, but they recognise he made a solid contribution in his solitary campaign at the club.

"I would like to thank Sebastian for his achievements," said Bayern chief executive Karl-Heinz Rummenigge.

"He has played an important part in winning the sixth title in succession last season. We wish Sebastian all the best for his future."